5j(6+j)=45

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Solution for 5j(6+j)=45 equation: 


Simplifying
5j(6 + j) = 45
(6 * 5j + j * 5j) = 45
(30j + 5j2) = 45

Solving
30j + 5j2 = 45

Solving for variable 'j'.

Reorder the terms:
-45 + 30j + 5j2 = 45 + -45

Combine like terms: 45 + -45 = 0
-45 + 30j + 5j2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-9 + 6j + j2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-9 + 6j + j2)' equal to zero and attempt to solve:

Simplifying
-9 + 6j + j2 = 0

Solving
-9 + 6j + j2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + 6j + 9 + j2 = 0 + 9

Reorder the terms:
-9 + 9 + 6j + j2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + 6j + j2 = 0 + 9
6j + j2 = 0 + 9

Combine like terms: 0 + 9 = 9
6j + j2 = 9

The j term is 6j.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6j + 9 + j2 = 9 + 9

Reorder the terms:
9 + 6j + j2 = 9 + 9

Combine like terms: 9 + 9 = 18
9 + 6j + j2 = 18

Factor a perfect square on the left side:
(j + 3)(j + 3) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(j + 3) equal to 4.242640687 and -4.242640687.


Subproblem 1
j + 3 = 4.242640687

Simplifying
j + 3 = 4.242640687

Reorder the terms:
3 + j = 4.242640687

Solving
3 + j = 4.242640687

Solving for variable 'j'.

Move all terms containing j to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + j = 4.242640687 + -3

Combine like terms: 3 + -3 = 0
0 + j = 4.242640687 + -3
j = 4.242640687 + -3

Combine like terms: 4.242640687 + -3 = 1.242640687
j = 1.242640687

Simplifying
j = 1.242640687


Subproblem 2
j + 3 = -4.242640687

Simplifying
j + 3 = -4.242640687

Reorder the terms:
3 + j = -4.242640687

Solving
3 + j = -4.242640687

Solving for variable 'j'.

Move all terms containing j to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + j = -4.242640687 + -3

Combine like terms: 3 + -3 = 0
0 + j = -4.242640687 + -3
j = -4.242640687 + -3

Combine like terms: -4.242640687 + -3 = -7.242640687
j = -7.242640687

Simplifying
j = -7.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {1.242640687, -7.242640687}
Solution
j = {1.242640687, -7.242640687}

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